To apply the traditional marginal-cost pricing to drive a user
equilibrium of the oligopolistic game to the system optimum, it
requires to classify the users into different classes and then
charge discriminatory tolls across user classes. By realizing the
difficulty of discriminating users when they differ in some
unobservable ways, Yang and Zhang investigated existence of
anonymous link tolls for transportation networks recently. In this
paper, we consider the anonymous link tolls for the oligopolistic
game with nonseparable, nonlinear and asymmetric cost functions with
fixed demands. With similar techniques developed by Yang and Zhang,
we first prove the existence of anonymous link tolls to decentralize
the system optimum to a user equilibrium. Then, by deriving some
bounds on the so-called price of anarchy, we analyze the efficiency
of such a toll strategy when the tolls are considered as part of the
system cost.